An Analysis of Wave Convection of Rolling Bodies

Abstract

A bond graph model of wave convection of rolling bodies is developed. The governing non-linear state space equations are derived directly from the bond graph and solved numerically for various system parameters and driving frequencies. Results include the motion-time history of the uniform spherical bodies treated herein as they traverse the “singulation wave.” Critical speeds and frequencies are identified. These results typify the singulation process for various fruits and vegetables. It is shown that the moving belt can be closely approximated by a rigid sine wave translating at wave speed. This leads to the derivation of a simple energy based design criterion for critical frequencies. The inclusion of damping in the model lowers the critical frequencies and allows for accurate prediction of experimentally measured critical frequencies.